# Data-driven Structured Realization

arXiv: https://arxiv.org/abs/1611.02072 · HTML: https://mlsanity.com/paper/1611.02072/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2016.

## Built on by (most cited first, 11 of 11)

- [Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference](https://mlsanity.com/paper/2107.02597/) (2021)
- [On the sample complexity of stabilizing linear dynamical systems from data](https://mlsanity.com/paper/2203.00474/) (2022)
- [Operator inference of non-Markovian terms for learning reduced models from partially observed state trajectories](https://mlsanity.com/paper/2103.01362/) (2021)
- [Context-aware controller inference for stabilizing dynamical systems from scarce data](https://mlsanity.com/paper/2207.11049/) (2022)
- [Nonlinear embeddings for conserving Hamiltonians and other quantities with Neural Galerkin schemes](https://mlsanity.com/paper/2310.07485/) (2023)
- [System stabilization with policy optimization on unstable latent manifolds](https://mlsanity.com/paper/2407.06418/) (2024)
- [Rank-Minimizing and Structured Model Inference](https://mlsanity.com/paper/2302.09521/) (2023)
- [Nonlinear model reduction for transport-dominated problems](https://mlsanity.com/paper/2602.01397/) (2026)
- [Active Sampling of Interpolation Points to Identify Dominant Subspaces for Model Reduction](https://mlsanity.com/paper/2409.03892/) (2024)
- [An adaptive data sampling strategy for stabilizing dynamical systems via controller inference](https://mlsanity.com/paper/2506.01816/) (2025)
- [Second-order AAA algorithms for structured data-driven modeling](https://mlsanity.com/paper/2506.02241/) (2025)

## Abstract (arXiv)

We present a framework for constructing structured realizations of linear dynamical systems having transfer functions of the form C(sumk=1K hk(s)Ak)-1B where h1,h2,ldots,hK are prescribed functions that specify the surmised structure of the model. Our construction is data-driven in the sense that an interpolant is derived entirely from measurements of a transfer function. Our approach extends the Loewner realization framework to more general system structure that includes second-order (and higher) systems as well as systems with internal delays. Numerical examples demonstrate the advantages of this approach.